On construction of images of layered media in inverse scattering problems for the wave equation of acoustics

Two-dimensional inverse scattering problems for the wave equation of acoustics on determining the density and acoustic impedance of the medium were studied. A necessary and sufficient condition for the unique solvability of these problems in the form of the energy conservation law is established. It is proved that this condition is that for each pulse oscillation source, located on the boundary of the half-plane, the flow of energy of the scattered waves is less than the energy flux of waves propagating from the boundary of the half-plane. This shows that the inverse scattering problems of dynamic acoustics and geophysics in the case of the law of conservation of energy is possible to determine the elastic-density parameters of the medium. The results allow to considerably extend the class of mathematical models currently used in the solution of multidimensional inverse scattering problems. Several special questions of interpretation for solutions of inverse problems are regarded.